My oldest, who returns to school this week, began learning multiplication two years ago in the third grade. But they don’t require them to memorize them anymore, apparently. This summer, I decided he was memorizing those multiplication tables before starting fifth grade. Mind you, his grades in math are fine. But as he moved into division this past year, I could see it was harder than it had to be. Do you remember chanting the times tables as a class? It was boring as anything, but knowing those facts make everything that comes after easier. My son, however, was really resistant to memorizing them. Eventually, early this summer, he was able to verbalize why: “I want to figure out the answer on my own.”

A-ha! He thought that memorization was somehow akin to cheating. I picked a neutral time–we were alone in the car together, on the way to the supermarket–to try to explain my reasoning to him. I told him that if he didn’t understand the process of multiplication, if he didn’t realize that 8×3 was the same as 8+8+8, then I wouldn’t want him memorizing the facts. Facts without understanding is no good. But he does understand the process, and now it was time to know these facts so well that his brain isn’t wasting time with 8+8+8, it just spits out 24. Just like he doesn’t have to start from A just to know what letter comes after T–he memorized the alphabet in order a long time ago without even thinking about it. That’s not cheating, he agreed.

He thought this over for a bit, and then he said, “I think writing them out would be a good way to memorize them. Often when I write myself a note so I don’t forget something, I end up not needing the note because writing it down made me remember it.” I told him I thought that was an excellent start, and chose not to remind him that I’d suggested this months ago and he refused. He needed to understand why he was doing this, and I was glad he came up with this strategy on his own.

Once he understood, the rest was relatively easy, because he was on board. I’d read somewhere to group the like tables, so we started with the 2s (easy), and followed that with the 4s and 8s. He wrote out the table, and I quizzed him with flash cards. I got out our Cuisenaire rods and we grouped them different ways to see how 2s, 4s, and 8s are related. Then we moved on to 3s, then 6s, then 9s, and finally 12s. I reminded him to use what he knew–if 7×2 is 14, then 7×12 has to end in a 4. If he wasn’t coming up with 12×8, I’d ask him 10×8 and then 2×8 before repeating 12×8. We left the 7s for last, because they’re not really related to anything else, but we’d covered everything in them by then, at least. (5s, 10s, and 11s didn’t need much work at all.)

They’ll need to be reinforced, of course, to make sure they stick. Sometimes I just ask him multiplication questions out of the blue, which has led to my youngest randomly stringing numbers together into math problems for us to answer. I wouldn’t have said I’m a fan of rote memorization, but it turned out I felt strongly that he should know these, really know them. Again, if he didn’t understand what multiplication is, I wouldn’t want him memorizing facts with no understanding. But I can also remember having to memorize oral presentations when I was just a little older than he is, and it certainly trained my mind in a certain way. Maybe next summer we’ll memorize some poetry…

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